Using L'Hospital's rule, can anyone solve this problem?

Question

= x^2 + 3, if x < 0
= 0, if x = 0
f(x) = x^2 - 3 if 0 < x < 2
= 1 if x = 2
= x^3 - 7 if 2 < x.
Then lim ........................ f(x) =
x=>0+

Answer 1

you cannot use L'Hopital's rule for this problem

the limit x-->0+ f(x) = lim x-->0+ x^2-3 =-3

Answer 2

I racked through my brains and I couldn't concieve of a way you could possibly use l'hopital's rule on this problem.

If you wanted to figure out the limit of the function as it approaches 0 from the positive side, then you would have to find the appropriate partial. In this case, f(x) = x^2 - 3.

This is logically continuous as it approaches 0, so lim[x->0] = (0)^2 - 3 = -3.

Therefore the limit = -3.

This is a special question in that the limit does not equal the value of the function (0) at that point.

Answer 3

Teds answer is inaccurate. at the start, one does no longer educate a particular by-product through a numeric argument. That lacks rigor and isn't perfect for an rationalization. Secondly, there are different strategies to educate that the by-product d/dx e^x is an analogous as e^x. The decrease definition you've shown isn't solvable. even with the reality that it truly is the decrease definition of the by-product, i understand of no thanks to extremely simplify that decrease into the most suitable predicted answer. The evidence of the by-product is achieved making use of alternative techniques, and so at the same time as someone strategies this decrease after the actual reality, the by-product of e^x is in reality already prevalent. are you able to remedy the issue? certain. you could remedy the issue making use of the rule of thumb. there is not any stipulation in math that you won't be able to. Even in circumstances the position Teds concerns are warranted, that one is presuming the resultant, there continues to be a huge difference to be made the following. think for the sake of argument that you're making use of the resultant of the answer/evidence to remedy the issue. there's a huge difference between proving a clean relationship it truly is not any longer already regularly occurring, and easily making use of a prevalent rule (whose evidence is per chance forgotten) to remedy a situation. fixing issues and proving theorems are distinct lines of wondering. you could remedy any situation making use of any regularly occurring rule (such as making use of l'Hôpital's Rule to judge the decrease definition of a spinoff), yet you won't be able to educate the rule of thumb making use of the rule of thumb even if it truly is not already prevalent to be authentic.

Answer 4

-3

Answer 5

limf(x)-f(0)/x-0= lim(x^2-3)'/x'= lim=2x=0

Answer 6

Can I solve this? Answer is no.